7 problems

Gieseker's irreducibility conjecture. The Floquet surface of $A$ is irreducible for every value of the spectral parameter $lambda$.

Conjugate-operator conjecture. There exists such a conjugate operator $\mathbb{A}(n)$ for which the Mourre estimate for $\Delta$ holds with respect to $\mathbb{A}(n)$ for every…

Threshold convergence-rate conjecture. The thresholds satisfy

Let $H$ be a periodic discrete Schrödinger operator as in, with periodic potential coefficients $\{c_{ik}\}$. Discrete Bethe–Sommerfeld conjecture. For small enough potentials…

Let $G$ be a simple graph, let $\mathcal{A}_G$ be the closure of its adjacency matrix initially defined on finitely supported functions, and let $\eta(\mathcal{A}_G)$ denote its de…

Let $d\geq 2$, let $q\neq 0$ be sign-definite, and let $\omega^{\ast}$ denote the periodic configuration associated with the extremal spectral values $E_{min}$ and $E_{max}$. A per…

Let $G$ be a locally finite unoriented simple graph, and let $A_G$ denote its adjacency matrix, viewed as a symmetric operator on the complex Hilbert space of square-summable funct…